Simple Linearizations of the Simple Pendulum for Any Amplitude∗

نویسنده

  • M. I. Molina
چکیده

Two simple, interpolatory-like linearizations are shown for the simple pendulum which can be used for any initial amplitude.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Numerical solution of higher index DAEs using their IAE's structure: Trajectory-prescribed path control problem and simple pendulum

In this paper, we solve higher index differential algebraic equations (DAEs) by transforming them into integral algebraic equations (IAEs). We apply collocation methods on continuous piece-wise polynomials space to solve the obtained higher index IAEs. The efficiency of the given method is improved by using a recursive formula for computing the integral part. Finally, we apply the obtained algo...

متن کامل

Analytical Solution of Differential Equation Associated with Simple Pendulum

Abstract In the present work, we provide the exact equation of motion of a simple pendulum of arbitrary amplitude. For first time, a new and exact expression is obtained for the time “t” of swinging of a simple pendulum from the vertical position to an arbitrary angular position “θ”. The time period “T” of such a pendulum is also exactly expressible in terms of hypergeometric functions.

متن کامل

NORMAL FORM SOLUTION OF REDUCED ORDER OSCILLATING SYSTEMS

This paper describes a preliminary investigation into the use of normal form theory for modelling large non-linear dynamical systems. Limit cycle oscillations are determined for simple two-degree-of-freedom double pendulum systems. The double pendulum system is reduced into its centre manifold before computing normal forms. Normal forms are obtained using a period averaging method which is appl...

متن کامل

Using the Adaptive Frequency Nonlinear Oscillator for Earning an Energy Efficient Motion Pattern in a Leg- Like Stretchable Pendulum by Exploiting the Resonant Mode

In this paper we investigate a biological framework to generate and adapt a motion pattern so that can be energy efficient. In fact, the motion pattern in legged animals and human emerges among interaction between a central pattern generator neural network called CPG and the musculoskeletal system. Here, we model this neuro - musculoskeletal system by means of a leg - like mechanical system cal...

متن کامل

Long-time behaviour of discretizations of the simple pendulum equation

We compare the performance of several discretizations of simple pendulum equation in a series of numerical experiments. The stress is put on the long-time behaviour. We choose for the comparison numerical schemes which preserve the qualitative features of solutions (like periodicity). All these schemes are either symplectic maps or integrable (preserving the energy integral) maps, or both. We d...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1997